Sequences & series worksheet with answers

Free printable Sequences & series worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
kSn​12345678910S = ?

Find the sum S of the infinite series Σk=1∞ 6·(−1/4)ᵏ.

a = 6r = −1/4k₀ = 1
S =
2.Easy
kak​123456789

Find the sum S9 of the first 9 terms of the geometric sequence 5, 2.5, 1.25, …

a₁ = 5r = 0.5n = 9
S9 =
3.Medium
k|aₖ₊₁/aₖ|123456789101112

Apply the ratio test to Σk=1∞ 3ᵏ·k!/kᵏ. Find L = lim |ak+1/ak|.

ak = 3ᵏ·k!/kᵏ
L =
4.Medium
AΣ (3/5)ᵏk = 1 … ∞BΣ 1/k²k = 1 … ∞CΣ k/(k + 7)k = 1 … ∞DΣ 1/(k² + 6)k = 1 … ∞

Exactly one of the four series diverges. Click it.

A: Σ (3/5)ᵏB: Σ 1/k²C: Σ k/(k + 7)D: Σ 1/(k² + 6)
  1. 1A: Σ (3/5)ᵏ
  2. 2B: Σ 1/k²
  3. 3C: Σ k/(k + 7)
  4. 4D: Σ 1/(k² + 6)
5.Hard

Recognise the series and find its sum: S = Σk=0∞ 1.5ᵏ/k!.

ak = 1.5ᵏ/k!
S =
6.Hard

Recognise the series and find its sum: S = Σk=1∞ k·0.25ᵏ.

ak = k·0.25ᵏ
S =

Answer key

  1. 1. S = −1.2
  2. 2. S9 = 9.98
  3. 3. L = 1.104
  4. 4. C: Σ k/(k + 7)
  5. 5. S = 4.482
  6. 6. S = 0.4444

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